Modular curves of genus 2

González-Jiménez, Enrique; González, Josep

doi:10.1090/S0025-5718-02-01458-8

Modular curves of genus 2
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by Enrique González-Jiménez and Josep González PDF

Math. Comp. 72 (2003), 397-418 Request permission

Abstract:

We prove that there are exactly $149$ genus two curves $C$ defined over $\mathbb {Q}$ such that there exists a nonconstant morphism $\pi :X_1(N)\rightarrow C$ defined over $\mathbb {Q}$ and the jacobian of $C$ is $\mathbb {Q}$-isogenous to the abelian variety $A_f$ attached by Shimura to a newform $f\in S_2(\Gamma _1(N))$. We determine the corresponding newforms and present equations for all these curves.

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